Holographic Realization of Riemann Zeros via a Hilbert-P´olya Operator
Year: 2025
Type: article
Abstract: We propose an exploratory operator model that realizes the imagi- nary parts of the non-trivial Riemann zeta zeros as the eigenvalues of a Schrödinger-type Hermitian operator, inspired by the spectral duality in AdS/CFT holography. The potential of the operator is derived from the AdS/CFT framework, specifically through the boundary projection of bulk quasi-normal modes (QNMs). We compute the eigenvalues using a finite-difference method, achieving a relative error of less than 0.2% for the first 100 Riemann zeros. The spectral trace and associated zeta func- tion are analyzed, showing a numerical correspondence with the Riemann zeta function. This framework, while exploratory, provides a concrete realization of the Hilbert-Pólya conjecture within a holographic context, supported by detailed numerical validations. This work builds on our previous AdS/CFT framework [5].
Author: Li, Y.Y.N.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6911913587
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